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POINT DECISIONS FOR INTERVAL–IDENTIFIED PARAMETERS

Published online by Cambridge University Press:  29 January 2014

Kyungchul Song
Kyungchul Song*
Affiliation:
University of British Columbia
*
*Address Correspondence to Kyungchul Song, Department of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC, Canada, V6T 1Z1; e-mail: kysong@mail.ubc.edu.
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Abstract

This paper considers a decision maker who prefers to make a point decision when the object of interest is interval-identified with regular bounds. When the bounds are just identified along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an efficient lower bound estimator plus the half of the known interval length. However, when the interval length or any nontrivial upper bound for the length is not known, the minimax approach suffers from triviality because the maximal risk is associated with infinitely long identified intervals. In this case, this paper proposes a local asymptotic minimax regret approach and shows that the midpoint between semiparametrically efficient bound estimators is optimal.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 2 , April 2014 , pp. 334 - 356
Copyright
Copyright © Cambridge University Press 2013 

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